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 A072450 Continued fraction expansion of the limit of a nested radical, sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ... )))). 1
 1, 1, 3, 7, 1, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 2, 20, 1, 2, 2, 2, 1, 2, 1, 1, 6, 2, 8, 5, 13, 2, 3, 1, 1, 115, 1, 4, 38, 4, 3, 1, 2, 1, 1, 1, 14, 1, 10, 4, 4, 5, 2, 2, 3, 19, 1, 1, 1, 5, 2, 1, 4, 1, 3, 1, 3, 4, 1, 8, 47, 33, 1, 1, 5, 13, 1, 14, 1, 5, 1, 1, 2, 17, 2, 1, 108, 9, 16, 3, 1, 2, 2, 3, 1, 5, 6, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Sqrt(1 + Sqrt(2 + Sqrt(3 + Sqrt(4 + ... = 1.75793275661800... Increasing partial continued fractions of the above are 1, 3, 7, 20, 115, 233, 301, 328, 16902, ... REFERENCES Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 & 229. David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, London, England, 1997, page 30. LINKS Eric Weisstein's World of Mathematics, Nested Radical. MATHEMATICA ContinuedFraction[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Range[100]]], 100] CROSSREFS Cf. A072449. Sequence in context: A295043 A074051 A048292 * A085785 A200235 A127929 Adjacent sequences:  A072447 A072448 A072449 * A072451 A072452 A072453 KEYWORD cofr,nonn AUTHOR Robert G. Wilson v, Aug 01 2002 STATUS approved

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Last modified June 26 20:24 EDT 2019. Contains 324380 sequences. (Running on oeis4.)